Opponents of President Viktor Yanukovych in Ukraine's deadlocked parliament are set to begin work on a draft bill on constitutional changes to dilute presidential powers.

Backed by street protesters, opposition leaders want a return to the constitution of 2004, when more power was in the hands of the parliament, rather than the president.

Yanukovych and his supporters, who have a majority in parliament, oppose such changes.

Addressing tens of thousands of antigovernment demonstrators in Kyiv on February 9, Vitali Klitschko repeated opposition demands for constitutional reforms and snap elections.

"[President Yanukovych] says we need half a year to get a new constitution," Klitschko said, "but our people are not going to wait for half a year. We can change the constitution now, go back to the 2004 constitution first, and then take time to draft a new constitution. But this in itself is not enough. People demand one thing -- snap presidential elections."

Far-right nationalist Oleh Tyahnybok attacked Russia's influence over Yanukovych, who met with Russian President Vladimir Putin on the sidelines of the Sochi Winter Olympics on February 7.

He has since returned to Kyiv, but no word has yet filtered out on what the two leaders discussed.

Elsewhere, Ukraine's security agency on February 9 warned of an alleged heightened risk of terrorism.

It said it was putting its counterterrorism units on alert, saying international airports, train, and bus stations, as well as power plants were particularly at risk. It also warned the seizure of government buildings would be viewed as manifestations of terrorism.

Antigovernment protesters have set up barricades in Kyiv's Independence Square and occupied several government buildings in the Ukrainian capital and elsewhere.

At least three activists were killed in violent clashes between protesters and riot police last month in Kyiv. Another was found dead outside Kyiv after being kidnapped from a hospital and reportedly tortured.

The antigovernment protests in Ukraine began in November after Yanukovych pulled back from a trade and association agreement with the European Union.

They have expanded since into mass demonstrations against perceived misrule and corruption under Yanukovych.